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Simulation of fiber-reinforced viscoelastic structures subjected to finite strains: multiplicative approach. / Tagiltsev, I. I.; Laktionov, P. P.; Shutov, A. V.

In: Meccanica, Vol. 53, No. 15, 01.12.2018, p. 3779-3794.

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@article{96e384a7bf8742e2b38525bdcc435ed8,
title = "Simulation of fiber-reinforced viscoelastic structures subjected to finite strains: multiplicative approach",
abstract = "The study is devoted to the geometrically nonlinear simulation of fiber-reinforced composite structures. The applicability of the multiplicative approach to the simulation of viscoelastic properties of a composite material is assessed, certain improvements are suggested. For a greater accuracy in applications involving local compressive fiber buckling, a new family of hyperelastic potentials is introduced. This family allows us to account for the variable critical compressive stress, which depends on the fiber-matrix interaction. For the simulation of viscoelasticity, the well-established Sidoroff decomposition of the deformation gradient is implemented. To account for the viscosity of the matrix material, the model of Simo and Miehe (Comput Methods Appl Mech Eng 98:41–104, 1992) is used; highly efficient iteration-free algorithms are implemented. The viscosity of the fiber is likewise described by the multiplicative decomposition of the deformation gradient, leading to a scalar differential equation; an efficient iteration-free algorithm is proposed for the implicit time stepping. The accuracy and convergence of the new iteration-free method is tested and compared to that of the standard scheme implementing the Newton iteration. To demonstrate the applicability of the approach, a pressurized multi-layer composite pipe is modelled; the so-called stretch inversion phenomenon is reproduced and explained. The stress distribution is obtained by a semi-analytical procedure; it may serve as a benchmark for FEM computations. Finally, the issue of the parameter identification is addressed.",
keywords = "Efficient numerics, Fiber-reinforced composite, Hyperelasticity, Large strain, Multiplicative decomposition, Viscoelasticity, BEHAVIOR, FIELD, STATE, COMPOSITES, MODEL, LINEAR VISCOELASTICITY, FORMULATION, MECHANICS, ARTERIES, FREE-ENERGY",
author = "Tagiltsev, {I. I.} and Laktionov, {P. P.} and Shutov, {A. V.}",
year = "2018",
month = dec,
day = "1",
doi = "10.1007/s11012-018-0909-0",
language = "English",
volume = "53",
pages = "3779--3794",
journal = "Meccanica",
issn = "0025-6455",
publisher = "Springer Netherlands",
number = "15",

}

RIS

TY - JOUR

T1 - Simulation of fiber-reinforced viscoelastic structures subjected to finite strains: multiplicative approach

AU - Tagiltsev, I. I.

AU - Laktionov, P. P.

AU - Shutov, A. V.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - The study is devoted to the geometrically nonlinear simulation of fiber-reinforced composite structures. The applicability of the multiplicative approach to the simulation of viscoelastic properties of a composite material is assessed, certain improvements are suggested. For a greater accuracy in applications involving local compressive fiber buckling, a new family of hyperelastic potentials is introduced. This family allows us to account for the variable critical compressive stress, which depends on the fiber-matrix interaction. For the simulation of viscoelasticity, the well-established Sidoroff decomposition of the deformation gradient is implemented. To account for the viscosity of the matrix material, the model of Simo and Miehe (Comput Methods Appl Mech Eng 98:41–104, 1992) is used; highly efficient iteration-free algorithms are implemented. The viscosity of the fiber is likewise described by the multiplicative decomposition of the deformation gradient, leading to a scalar differential equation; an efficient iteration-free algorithm is proposed for the implicit time stepping. The accuracy and convergence of the new iteration-free method is tested and compared to that of the standard scheme implementing the Newton iteration. To demonstrate the applicability of the approach, a pressurized multi-layer composite pipe is modelled; the so-called stretch inversion phenomenon is reproduced and explained. The stress distribution is obtained by a semi-analytical procedure; it may serve as a benchmark for FEM computations. Finally, the issue of the parameter identification is addressed.

AB - The study is devoted to the geometrically nonlinear simulation of fiber-reinforced composite structures. The applicability of the multiplicative approach to the simulation of viscoelastic properties of a composite material is assessed, certain improvements are suggested. For a greater accuracy in applications involving local compressive fiber buckling, a new family of hyperelastic potentials is introduced. This family allows us to account for the variable critical compressive stress, which depends on the fiber-matrix interaction. For the simulation of viscoelasticity, the well-established Sidoroff decomposition of the deformation gradient is implemented. To account for the viscosity of the matrix material, the model of Simo and Miehe (Comput Methods Appl Mech Eng 98:41–104, 1992) is used; highly efficient iteration-free algorithms are implemented. The viscosity of the fiber is likewise described by the multiplicative decomposition of the deformation gradient, leading to a scalar differential equation; an efficient iteration-free algorithm is proposed for the implicit time stepping. The accuracy and convergence of the new iteration-free method is tested and compared to that of the standard scheme implementing the Newton iteration. To demonstrate the applicability of the approach, a pressurized multi-layer composite pipe is modelled; the so-called stretch inversion phenomenon is reproduced and explained. The stress distribution is obtained by a semi-analytical procedure; it may serve as a benchmark for FEM computations. Finally, the issue of the parameter identification is addressed.

KW - Efficient numerics

KW - Fiber-reinforced composite

KW - Hyperelasticity

KW - Large strain

KW - Multiplicative decomposition

KW - Viscoelasticity

KW - BEHAVIOR

KW - FIELD

KW - STATE

KW - COMPOSITES

KW - MODEL

KW - LINEAR VISCOELASTICITY

KW - FORMULATION

KW - MECHANICS

KW - ARTERIES

KW - FREE-ENERGY

UR - http://www.scopus.com/inward/record.url?scp=85055703456&partnerID=8YFLogxK

U2 - 10.1007/s11012-018-0909-0

DO - 10.1007/s11012-018-0909-0

M3 - Article

AN - SCOPUS:85055703456

VL - 53

SP - 3779

EP - 3794

JO - Meccanica

JF - Meccanica

SN - 0025-6455

IS - 15

ER -

ID: 17246751